Wave-function-based operator optimization for two-hadron systems in lattice QCD

A systematic way to constructing optimized interpolating operators for two-hadron systems is developed by incorporating interhadron spatial wave functions. The wave functions can be obtained from an iterative process with an appropriate initial guess. To implement these operators, a novel quark smearing technique utilizing <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>Z</a:mi> <a:mn>3</a:mn> </a:msub> </a:math> noise vectors is proposed, which allows for effectively incorporating interhadron spatial wave functions at the source without using all-to-all quark propagators. Proof-of-principle application to the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msub> <c:mi mathvariant="normal">Ω</c:mi> <c:mrow> <c:mi>c</c:mi> <c:mi>c</c:mi> <c:mi>c</c:mi> </c:mrow> </c:msub> <c:msub> <c:mi mathvariant="normal">Ω</c:mi> <c:mrow> <c:mi>c</c:mi> <c:mi>c</c:mi> <c:mi>c</c:mi> </c:mrow> </c:msub> </c:math> system using physical-point lattice configurations with a large size <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>L</g:mi> <g:mi>a</g:mi> <g:mo>≃</g:mo> <g:mn>8.1</g:mn> <g:mtext> </g:mtext> <g:mtext> </g:mtext> <g:mi>fm</g:mi> </g:math> demonstrates that optimized operators outperform combinations of limited plane wave operators in the variational analysis, enabling clear identification of states around <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mn>2</i:mn> <i:msub> <i:mi>m</i:mi> <i:msub> <i:mi mathvariant="normal">Ω</i:mi> <i:mrow> <i:mi>c</i:mi> <i:mi>c</i:mi> <i:mi>c</i:mi> </i:mrow> </i:msub> </i:msub> <i:mo>≃</i:mo> <i:mn>9700</i:mn> <i:mtext> </i:mtext> <i:mtext> </i:mtext> <i:mi>MeV</i:mi> </i:math> with the energy gap as narrow as <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"> <l:mo>∼</l:mo> <l:mn>5</l:mn> <l:mtext> </l:mtext> <l:mtext> </l:mtext> <l:mi>MeV</l:mi> </l:math> . A comparison on correlation functions, effective energies, and HAL QCD potentials between unoptimized operators and optimized operators is given, with a special emphasis on the effects from nearby elastic scattering states. Potential applicability of the optimized operator to various two-hadron systems and its relation to the variational method are also discussed.